Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.02\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.02))) (- (* x y) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.02)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 0.02d0))) then
        tmp = (x * y) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.02)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.02):
		tmp = (x * y) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.02))
		tmp = Float64(Float64(x * y) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.02)))
		tmp = (x * y) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.02]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.0200000000000000004 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.1%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   4. Step-by-step derivation

      1. *-commutative 98.1%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   5. Simplified 98.1%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   if -1 < x < 0.0200000000000000004

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{y} - x \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.02\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-105}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e-105) y (if (<= y 1.2e-20) (- x) (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e-105) {
		tmp = y;
	} else if (y <= 1.2e-20) {
		tmp = -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.5d-105)) then
        tmp = y
    else if (y <= 1.2d-20) then
        tmp = -x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.5e-105) {
		tmp = y;
	} else if (y <= 1.2e-20) {
		tmp = -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e-105:
		tmp = y
	elif y <= 1.2e-20:
		tmp = -x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e-105)
		tmp = y;
	elseif (y <= 1.2e-20)
		tmp = Float64(-x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.5e-105)
		tmp = y;
	elseif (y <= 1.2e-20)
		tmp = -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e-105], y, If[LessEqual[y, 1.2e-20], (-x), N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999982e-105

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.7%

      \[\leadsto \color{blue}{y} - x \]
   4. Step-by-step derivation

      1. sub-neg 72.7%

         \[\leadsto \color{blue}{y + \left(-x\right)} \]

      2. add-sqr-sqrt 36.2%

         \[\leadsto y + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

      3. sqrt-unprod 75.6%

         \[\leadsto y + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

      4. sqr-neg 75.6%

         \[\leadsto y + \sqrt{\color{blue}{x \cdot x}} \]

      5. sqrt-unprod 31.6%

         \[\leadsto y + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

      6. add-sqr-sqrt 62.8%

         \[\leadsto y + \color{blue}{x} \]

   5. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{y + x} \]

   6. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{y} \]

   if -2.49999999999999982e-105 < y < 1.19999999999999996e-20

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + 1\right) \cdot y + \left(-x\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot \left(x + 1\right)} + \left(-x\right) \]

      3. +-commutative 100.0%

         \[\leadsto y \cdot \color{blue}{\left(1 + x\right)} + \left(-x\right) \]

      4. distribute-lft-in 100.0%

         \[\leadsto \color{blue}{\left(y \cdot 1 + y \cdot x\right)} + \left(-x\right) \]

      5. *-rgt-identity 100.0%

         \[\leadsto \left(\color{blue}{y} + y \cdot x\right) + \left(-x\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \color{blue}{y + \left(y \cdot x + \left(-x\right)\right)} \]

      7. *-commutative 100.0%

         \[\leadsto y + \left(\color{blue}{x \cdot y} + \left(-x\right)\right) \]

      8. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \left(-x\right)\right) + y} \]

      9. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{y \cdot x} + \left(-x\right)\right) + y \]

      10. neg-mul-1 100.0%

          \[\leadsto \left(y \cdot x + \color{blue}{-1 \cdot x}\right) + y \]

      11. distribute-rgt-out 100.0%

          \[\leadsto \color{blue}{x \cdot \left(y + -1\right)} + y \]

      12. fma-define 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.3%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 86.3%

         \[\leadsto \color{blue}{-x} \]

   7. Simplified 86.3%

      \[\leadsto \color{blue}{-x} \]

   if 1.19999999999999996e-20 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 51.4%

      \[\leadsto \color{blue}{y} - x \]
   4. Step-by-step derivation

      1. sub-neg 51.4%

         \[\leadsto \color{blue}{y + \left(-x\right)} \]

      2. add-sqr-sqrt 25.7%

         \[\leadsto y + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

      3. sqrt-unprod 59.7%

         \[\leadsto y + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

      4. sqr-neg 59.7%

         \[\leadsto y + \sqrt{\color{blue}{x \cdot x}} \]

      5. sqrt-unprod 26.3%

         \[\leadsto y + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

      6. add-sqr-sqrt 51.8%

         \[\leadsto y + \color{blue}{x} \]

   5. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-105}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.95e-103) y (if (<= y 4.2e-19) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.95e-103) {
		tmp = y;
	} else if (y <= 4.2e-19) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.95d-103)) then
        tmp = y
    else if (y <= 4.2d-19) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.95e-103) {
		tmp = y;
	} else if (y <= 4.2e-19) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.95e-103:
		tmp = y
	elif y <= 4.2e-19:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.95e-103)
		tmp = y;
	elseif (y <= 4.2e-19)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.95e-103)
		tmp = y;
	elseif (y <= 4.2e-19)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.95e-103], y, If[LessEqual[y, 4.2e-19], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9500000000000001e-103 or 4.1999999999999998e-19 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.8%

      \[\leadsto \color{blue}{y} - x \]
   4. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \color{blue}{y + \left(-x\right)} \]

      2. add-sqr-sqrt 31.3%

         \[\leadsto y + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

      3. sqrt-unprod 68.2%

         \[\leadsto y + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

      4. sqr-neg 68.2%

         \[\leadsto y + \sqrt{\color{blue}{x \cdot x}} \]

      5. sqrt-unprod 29.2%

         \[\leadsto y + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

      6. add-sqr-sqrt 57.6%

         \[\leadsto y + \color{blue}{x} \]

   5. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{y + x} \]

   6. Taylor expanded in y around inf 57.3%

      \[\leadsto \color{blue}{y} \]

   if -1.9500000000000001e-103 < y < 4.1999999999999998e-19

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + 1\right) \cdot y + \left(-x\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot \left(x + 1\right)} + \left(-x\right) \]

      3. +-commutative 100.0%

         \[\leadsto y \cdot \color{blue}{\left(1 + x\right)} + \left(-x\right) \]

      4. distribute-lft-in 100.0%

         \[\leadsto \color{blue}{\left(y \cdot 1 + y \cdot x\right)} + \left(-x\right) \]

      5. *-rgt-identity 100.0%

         \[\leadsto \left(\color{blue}{y} + y \cdot x\right) + \left(-x\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \color{blue}{y + \left(y \cdot x + \left(-x\right)\right)} \]

      7. *-commutative 100.0%

         \[\leadsto y + \left(\color{blue}{x \cdot y} + \left(-x\right)\right) \]

      8. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y + \left(-x\right)\right) + y} \]

      9. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{y \cdot x} + \left(-x\right)\right) + y \]

      10. neg-mul-1 100.0%

          \[\leadsto \left(y \cdot x + \color{blue}{-1 \cdot x}\right) + y \]

      11. distribute-rgt-out 100.0%

          \[\leadsto \color{blue}{x \cdot \left(y + -1\right)} + y \]

      12. fma-define 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.3%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 86.3%

         \[\leadsto \color{blue}{-x} \]

   7. Simplified 86.3%

      \[\leadsto \color{blue}{-x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- y x))

C

double code(double x, double y) {
	return y - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y - x
end function

Java

public static double code(double x, double y) {
	return y - x;
}

Python

def code(x, y):
	return y - x

Julia

function code(x, y)
	return Float64(y - x)
end

MATLAB

function tmp = code(x, y)
	tmp = y - x;
end

Wolfram

code[x_, y_] := N[(y - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0 77.6%

   \[\leadsto \color{blue}{y} - x \]
4. Add Preprocessing

Alternative 6: 38.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

public static double code(double x, double y) {
	return y;
}

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0 77.6%

   \[\leadsto \color{blue}{y} - x \]
4. Step-by-step derivation

   1. sub-neg 77.6%

      \[\leadsto \color{blue}{y + \left(-x\right)} \]

   2. add-sqr-sqrt 39.0%

      \[\leadsto y + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   3. sqrt-unprod 57.1%

      \[\leadsto y + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   4. sqr-neg 57.1%

      \[\leadsto y + \sqrt{\color{blue}{x \cdot x}} \]

   5. sqrt-unprod 19.8%

      \[\leadsto y + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   6. add-sqr-sqrt 40.0%

      \[\leadsto y + \color{blue}{x} \]

5. Applied egg-rr 40.0%

   \[\leadsto \color{blue}{y + x} \]

6. Taylor expanded in y around inf 40.5%

   \[\leadsto \color{blue}{y} \]
7. Add Preprocessing

Alternative 7: 2.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(x + 1\right) \cdot y + \left(-x\right)} \]

   2. *-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + 1\right)} + \left(-x\right) \]

   3. +-commutative 100.0%

      \[\leadsto y \cdot \color{blue}{\left(1 + x\right)} + \left(-x\right) \]

   4. distribute-lft-in 100.0%

      \[\leadsto \color{blue}{\left(y \cdot 1 + y \cdot x\right)} + \left(-x\right) \]

   5. *-rgt-identity 100.0%

      \[\leadsto \left(\color{blue}{y} + y \cdot x\right) + \left(-x\right) \]

   6. associate-+l+ 100.0%

      \[\leadsto \color{blue}{y + \left(y \cdot x + \left(-x\right)\right)} \]

   7. *-commutative 100.0%

      \[\leadsto y + \left(\color{blue}{x \cdot y} + \left(-x\right)\right) \]

   8. +-commutative 100.0%

      \[\leadsto \color{blue}{\left(x \cdot y + \left(-x\right)\right) + y} \]

   9. *-commutative 100.0%

      \[\leadsto \left(\color{blue}{y \cdot x} + \left(-x\right)\right) + y \]

   10. neg-mul-1 100.0%

       \[\leadsto \left(y \cdot x + \color{blue}{-1 \cdot x}\right) + y \]

   11. distribute-rgt-out 100.0%

       \[\leadsto \color{blue}{x \cdot \left(y + -1\right)} + y \]

   12. fma-define 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 39.0%

   \[\leadsto \color{blue}{-1 \cdot x} \]
6. Step-by-step derivation

   1. neg-mul-1 39.0%

      \[\leadsto \color{blue}{-x} \]

7. Simplified 39.0%

   \[\leadsto \color{blue}{-x} \]
8. Step-by-step derivation

   1. neg-sub0 39.0%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 39.0%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 19.3%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 19.4%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 19.4%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.2%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.7%

      \[\leadsto 0 + \color{blue}{x} \]

9. Applied egg-rr 2.7%

   \[\leadsto \color{blue}{0 + x} \]
10. Step-by-step derivation

    1. +-lft-identity 2.7%

       \[\leadsto \color{blue}{x} \]

11. Simplified 2.7%

    \[\leadsto \color{blue}{x} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))